Having just come out of a datastructures class, this is the view that seems the most useful to me. ADTs in general seem to be very well expressed with classes,

Having just come out of a datastructures class, this is the view that seems the most useful to me. ADTs in general seem to be very well expressed with classes, and I think it is exactly for the reason you mentioned: they are just systems that need to be able to define the ways in which a user is allowed to interact with the data.